1. Field of the Invention
The present invention is directed in general to field of information processing. In one aspect, the present invention relates to the generation of complex exponentials for use in frequency domain processing and time domain processing.
2. Description of the Related Art
Signal processing applications increasingly require the use of complex exponentials for different frequency domain and time domain applications. For example. 3GPP long term evolution (LTE) requires over 40 different sizes of Fourier transforms, such as Discrete Fourier Transforms (DFTs) and Fast Fourier Transforms (FFTs), which use complex exponentials to compute the Fourier transforms in the frequency domain. In computing such Fourier transforms, twiddle factors are generated as trigonometric constant coefficients that are typically stored in lookup tables and multiplied by the data being transformed. Complex exponentials may also be used in time domain applications, such as time domain mixer, which generate digital signals using a numerically controlled oscillator or other digital signal generator. While existing solutions have computed Fourier transforms by generating complex exponentials as twiddle factors that are stored in one or more look up tables, such solutions result in inefficient use of storage in signal processors, and are constrained to provide frequency domain solutions. And while there are other solutions which generate a scalar sequence of complex exponentials in the time domain, these solutions are not adapted to generate complex exponentials in the frequency domain. In any case, the real-time processing requirements for generating and using complex exponentials can impose significant complexity and processing costs in terms of the required digital processing resources.